Q-binomial convolution and transformations of Q-appell polynomials

Alaa Mohammed Obad; Asif Khan; Kottakkaran Sooppy Nisar; Ahmed Morsy

doi:10.3390/axioms10020070

Q-binomial convolution and transformations of Q-appell polynomials

Alaa Mohammed Obad, Asif Khan, Kottakkaran Sooppy Nisar, Ahmed Morsy

Aligarh Muslim University

Research output: Contribution to journal › Article › peer-review

8 Scopus citations

Abstract

In this paper, binomial convolution in the frame of quantum calculus is studied for the set A_q of q-Appell sequences. It has been shown that the set A_q of q-Appell sequences forms an Abelian group under the operation of binomial convolution. Several properties for this Abelian group structure A_q have been studied. A new definition of the q-Appell polynomials associated with a random variable is proposed. Scale transformation as well as transformation based on expectation with respect to a random variable is used to present the determinantal form of q-Appell sequences.

Original language	English
Article number	70
Journal	Axioms
Volume	10
Issue number	2
DOIs	https://doi.org/10.3390/axioms10020070
State	Published - Jun 2021

Keywords

Abelian group
Appell sequences transformation
Binomial convolution
Q-Appell polynomials
Q-calculus

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title = "Q-binomial convolution and transformations of Q-appell polynomials",

abstract = "In this paper, binomial convolution in the frame of quantum calculus is studied for the set Aq of q-Appell sequences. It has been shown that the set Aq of q-Appell sequences forms an Abelian group under the operation of binomial convolution. Several properties for this Abelian group structure Aq have been studied. A new definition of the q-Appell polynomials associated with a random variable is proposed. Scale transformation as well as transformation based on expectation with respect to a random variable is used to present the determinantal form of q-Appell sequences.",

keywords = "Abelian group, Appell sequences transformation, Binomial convolution, Q-Appell polynomials, Q-calculus",

author = "Obad, \{Alaa Mohammed\} and Asif Khan and Nisar, \{Kottakkaran Sooppy\} and Ahmed Morsy",

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AU - Khan, Asif

AU - Nisar, Kottakkaran Sooppy

AU - Morsy, Ahmed

PY - 2021/6

Y1 - 2021/6

N2 - In this paper, binomial convolution in the frame of quantum calculus is studied for the set Aq of q-Appell sequences. It has been shown that the set Aq of q-Appell sequences forms an Abelian group under the operation of binomial convolution. Several properties for this Abelian group structure Aq have been studied. A new definition of the q-Appell polynomials associated with a random variable is proposed. Scale transformation as well as transformation based on expectation with respect to a random variable is used to present the determinantal form of q-Appell sequences.

AB - In this paper, binomial convolution in the frame of quantum calculus is studied for the set Aq of q-Appell sequences. It has been shown that the set Aq of q-Appell sequences forms an Abelian group under the operation of binomial convolution. Several properties for this Abelian group structure Aq have been studied. A new definition of the q-Appell polynomials associated with a random variable is proposed. Scale transformation as well as transformation based on expectation with respect to a random variable is used to present the determinantal form of q-Appell sequences.

KW - Abelian group

KW - Appell sequences transformation

KW - Binomial convolution

KW - Q-Appell polynomials

KW - Q-calculus

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VL - 10

JO - Axioms

JF - Axioms

IS - 2

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ER -

Q-binomial convolution and transformations of Q-appell polynomials

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Keywords

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